--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/no_shm_selinux/Enrich2.thy Mon Dec 23 19:47:17 2013 +0800
@@ -0,0 +1,624 @@
+theory Enrich
+imports Main Flask Static Init_prop Valid_prop Tainted_prop Delete_prop Co2sobj_prop S2ss_prop S2ss_prop2
+ Temp Enrich
+begin
+
+context tainting_s begin
+
+lemma get_parentfs_ctxts_prop:
+ "\<lbrakk>get_parentfs_ctxts s (a # f) = Some ctxts; sectxt_of_obj s (O_dir f) = Some ctxt; valid s\<rbrakk>
+ \<Longrightarrow> ctxt \<in> set (ctxts)"
+apply (induct f)
+apply (auto split:option.splits)
+done
+
+lemma search_check_allp_intro:
+ "\<lbrakk>search_check s sp pf; get_parentfs_ctxts s pf = Some ctxts; valid s; is_dir s pf\<rbrakk>
+ \<Longrightarrow> search_check_allp sp (set ctxts)"
+apply (case_tac pf)
+apply (simp split:option.splits if_splits add:search_check_allp_def)
+apply (rule ballI)
+apply (auto simp:search_check_ctxt_def search_check_dir_def split:if_splits option.splits)
+apply (auto simp:search_check_allp_def search_check_file_def)
+apply (frule is_dir_not_file, simp)
+done
+
+lemma search_check_leveling_f:
+ "\<lbrakk>search_check s sp pf; parent f = Some pf; is_file s f; valid s;
+ sectxt_of_obj s (O_file f) = Some fctxt; search_check_file sp fctxt\<rbrakk>
+ \<Longrightarrow> search_check s sp f"
+apply (case_tac f, simp+)
+apply (auto split:option.splits simp:search_check_ctxt_def)
+apply (frule parentf_is_dir_prop2, simp)
+apply (erule get_pfs_secs_prop, simp)
+apply (erule_tac search_check_allp_intro, simp_all)
+apply (simp add:parentf_is_dir_prop2)
+done
+
+lemma enrich_proc_prop:
+ "\<lbrakk>valid s; is_created_proc s p; p' \<notin> all_procs s\<rbrakk>
+ \<Longrightarrow> valid (enrich_proc s p p') \<and>
+ (\<forall> obj. alive s obj \<longrightarrow> alive (enrich_proc s p p') obj) \<and>
+ (\<forall> obj. enrich_not_alive s obj \<longrightarrow> enrich_not_alive (enrich_proc s p p') obj) \<and>
+ (files_hung_by_del (enrich_proc s p p') = files_hung_by_del s) \<and>
+ (\<forall> tp. tp \<in> current_procs s \<longrightarrow> cp2sproc (enrich_proc s p p') tp = cp2sproc s tp) \<and>
+ (\<forall> f. f \<in> current_files s \<longrightarrow> cf2sfile (enrich_proc s p p') f = cf2sfile s f) \<and>
+ (\<forall> q. q \<in> current_msgqs s \<longrightarrow> cq2smsgq (enrich_proc s p p') q = cq2smsgq s q) \<and>
+ (\<forall> tp fd f. file_of_proc_fd s tp fd = Some f \<longrightarrow> file_of_proc_fd (enrich_proc s p p') tp fd = Some f) \<and>
+ (\<forall> tp fd flags. flags_of_proc_fd s tp fd = Some flags \<longrightarrow>
+ flags_of_proc_fd (enrich_proc s p p') tp fd = Some flags) \<and>
+ (\<forall> q. msgs_of_queue (enrich_proc s p p') q = msgs_of_queue s q) \<and>
+ (\<forall> tp fd. fd \<in> proc_file_fds s tp \<longrightarrow> cfd2sfd (enrich_proc s p p') tp fd = cfd2sfd s tp fd) \<and>
+ (cp2sproc (enrich_proc s p p') p' = cp2sproc s p) \<and>
+ (\<forall> fd. fd \<in> proc_file_fds s p \<longrightarrow> cfd2sfd (enrich_proc s p p') p' fd = cfd2sfd s p fd)"
+proof (induct s)
+ case Nil
+ thus ?case by (auto simp:is_created_proc_def)
+next
+ case (Cons e s)
+ hence vd_cons: "valid (e # s)" and created_cons: "is_created_proc (e # s) p"
+ and all_procs_cons: "p' \<notin> all_procs (e # s)" and vd: "valid s"
+ and os: "os_grant s e" and grant: "grant s e"
+ by (auto dest:vd_cons vt_grant_os vt_grant)
+ from all_procs_cons have all_procs: "p' \<notin> all_procs s" by (case_tac e, auto)
+ from Cons have pre: "is_created_proc s p \<Longrightarrow> valid (enrich_proc s p p') \<and>
+ (\<forall>obj. alive s obj \<longrightarrow> alive (enrich_proc s p p') obj) \<and>
+ (\<forall>obj. enrich_not_alive s obj \<longrightarrow> enrich_not_alive (enrich_proc s p p') obj) \<and>
+ files_hung_by_del (enrich_proc s p p') = files_hung_by_del s \<and>
+ (\<forall>tp. tp \<in> current_procs s \<longrightarrow> cp2sproc (enrich_proc s p p') tp = cp2sproc s tp) \<and>
+ (\<forall>f. f \<in> current_files s \<longrightarrow> cf2sfile (enrich_proc s p p') f = cf2sfile s f) \<and>
+ (\<forall>q. q \<in> current_msgqs s \<longrightarrow> cq2smsgq (enrich_proc s p p') q = cq2smsgq s q) \<and>
+ (\<forall>tp fd f. file_of_proc_fd s tp fd = Some f \<longrightarrow> file_of_proc_fd (enrich_proc s p p') tp fd = Some f) \<and>
+ (\<forall>tp fd flags.
+ flags_of_proc_fd s tp fd = Some flags \<longrightarrow> flags_of_proc_fd (enrich_proc s p p') tp fd = Some flags) \<and>
+ (\<forall>q. msgs_of_queue (enrich_proc s p p') q = msgs_of_queue s q) \<and>
+ (\<forall>tp fd. fd \<in> proc_file_fds s tp \<longrightarrow> cfd2sfd (enrich_proc s p p') tp fd = cfd2sfd s tp fd) \<and>
+ (cp2sproc (enrich_proc s p p') p' = cp2sproc s p) \<and>
+ (\<forall> fd. fd \<in> proc_file_fds s p \<longrightarrow> cfd2sfd (enrich_proc s p p') p' fd = cfd2sfd s p fd)"
+ using vd all_procs by auto
+ have alive_pre: "is_created_proc s p \<Longrightarrow> (\<forall>obj. alive s obj \<longrightarrow> alive (enrich_proc s p p') obj)"
+ using pre by simp
+ hence curf_pre: "is_created_proc s p \<Longrightarrow> (\<forall>f. f \<in> current_files s \<longrightarrow> f \<in> current_files (enrich_proc s p p'))"
+ using vd apply auto
+ apply (drule is_file_or_dir, simp)
+ apply (erule disjE)
+ apply (erule_tac x = "O_file f" in allE, simp add:is_file_in_current)
+ apply (erule_tac x = "O_dir f" in allE, simp add:is_dir_in_current)
+ done
+ have vd_enrich_cons: "valid (enrich_proc (e # s) p p')"
+ proof-
+ from pre have pre': "is_created_proc s p \<Longrightarrow> valid (enrich_proc s p p')" by simp
+ have "is_created_proc s p \<Longrightarrow> valid (e # enrich_proc s p p')"
+ apply (frule pre')
+ apply (erule_tac s = s in enrich_valid_intro_cons)
+ apply (simp_all add:os grant vd pre)
+ done
+ moreover have "\<And>f fds. \<lbrakk>valid (Execve p f fds # enrich_proc s p p'); is_created_proc s p;
+ valid (Execve p f fds # s); p' \<notin> all_procs s\<rbrakk>
+ \<Longrightarrow> valid (Execve p' f (fds \<inter> proc_file_fds s p) # Execve p f fds # enrich_proc s p p')"
+ proof-
+ fix f fds
+ assume a1: "valid (Execve p f fds # enrich_proc s p p')" and a2: "is_created_proc s p"
+ and a3: "valid (Execve p f fds # s)" and a0: "p' \<notin> all_procs s"
+ have cp2sp: "\<forall> tp. tp \<in> current_procs s \<longrightarrow> cp2sproc (enrich_proc s p p') tp = cp2sproc s tp"
+ and cf2sf: "\<forall> tf. tf \<in> current_files s \<longrightarrow> cf2sfile (enrich_proc s p p') tf = cf2sfile s tf"
+ and cfd2sfd: "\<forall> tp tfd. tfd \<in> proc_file_fds s tp \<longrightarrow> cfd2sfd (enrich_proc s p p') tp tfd = cfd2sfd s tp tfd"
+ and ffd_remain: "\<forall>tp fd f. file_of_proc_fd s tp fd = Some f \<longrightarrow>
+ file_of_proc_fd (enrich_proc s p p') tp fd = Some f"
+ and dup_sp: "cp2sproc (enrich_proc s p p') p' = cp2sproc s p"
+ and dup_sfd: "\<forall> fd. fd \<in> proc_file_fds s p \<longrightarrow> cfd2sfd (enrich_proc s p p') p' fd = cfd2sfd s p fd"
+ using pre a2 by auto
+ show "valid (Execve p' f (fds \<inter> proc_file_fds s p) # Execve p f fds # enrich_proc s p p')"
+ proof-
+ from a0 a3 have a0': "p' \<noteq> p" by (auto dest!:vt_grant_os not_all_procs_prop3)
+ from a3 have grant: "grant s (Execve p f fds)" and os: "os_grant s (Execve p f fds)"
+ by (auto dest:vt_grant_os vt_grant simp del:os_grant.simps)
+ have f_in: "is_file (enrich_proc s p p') f"
+ proof-
+ from pre a2
+ have a4: "\<forall> obj. alive s obj \<longrightarrow> alive (enrich_proc s p p') obj"
+ by (auto)
+ show ?thesis using a3 a4
+ apply (erule_tac x = "O_file f" in allE)
+ by (auto dest:vt_grant_os)
+ qed
+ moreover have a5: "proc_file_fds s p \<subseteq> proc_file_fds (Execve p f fds # enrich_proc s p p') p'"
+ using a3 a0'
+ apply (frule_tac vt_grant_os)
+ apply (auto simp:proc_file_fds_def)
+ apply (rule_tac x = fa in exI)
+ apply (erule enrich_proc_dup_ffd)
+ apply (simp_all add:vd all_procs a2)
+ done
+ ultimately have "os_grant (Execve p f fds # enrich_proc s p p') (Execve p' f (fds \<inter> proc_file_fds s p))"
+ apply (auto simp:is_file_simps enrich_proc_dup_in a2 vd all_procs a1 enrich_proc_dup_ffds)
+ done
+ moreover have "grant (Execve p f fds # enrich_proc s p p') (Execve p' f (fds \<inter> proc_file_fds s p))"
+ proof-
+ from grant obtain up rp tp uf rf tf
+ where p1: "sectxt_of_obj s (O_proc p) = Some (up, rp, tp)"
+ and p2: "sectxt_of_obj s (O_file f) = Some (uf, rf, tf)"
+ by (simp split:option.splits, blast)
+ with grant obtain pu nr nt where p3: "npctxt_execve (up, rp, tp) (uf, rf, tf) = Some (pu, nr, nt)"
+ by (simp split:option.splits del:npctxt_execve.simps, blast)
+ have p1': "sectxt_of_obj (Execve p f fds # enrich_proc s p p') (O_proc p') = Some (up, rp, tp)"
+ using p1 dup_sp a1 a0'
+ apply (simp add:sectxt_of_obj_simps)
+ by (simp add:cp2sproc_def split:option.splits)
+ from os have f_in': "is_file s f" by simp
+ from vd os have "\<exists> sf. cf2sfile s f = Some sf"
+ by (auto dest!:is_file_in_current current_file_has_sfile)
+ hence p2': "sectxt_of_obj (Execve p f fds # enrich_proc s p p') (O_file f) = Some (uf, rf, tf)"
+ using f_in p2 cf2sf os a1
+ apply (erule_tac x = f in allE)
+ apply (auto dest:is_file_in_current simp:cf2sfile_def sectxt_of_obj_simps split:option.splits)
+ apply (case_tac f, simp)
+ apply (drule_tac s = s in root_is_dir', simp add:vd, simp+)
+ done
+ from dup_sfd a5 have "\<forall>fd. fd \<in> proc_file_fds s p \<longrightarrow>
+ cfd2sfd (Execve p f fds # enrich_proc s p p') p' fd = cfd2sfd s p fd"
+ apply (rule_tac allI)
+ apply (erule_tac x = fd in allE, clarsimp)
+ apply (drule set_mp, simp)
+ apply (auto simp:cfd2sfd_execve proc_file_fds_def a1)
+ done
+ hence "inherit_fds_check (Execve p f fds # enrich_proc s p p') (up, nr, nt) p' (fds \<inter> proc_file_fds s p)"
+ using grant os p1 p2 p3 vd
+ apply (clarsimp)
+ apply (rule_tac s = s and p = p and fds = fds in enrich_inherit_fds_check_dup)
+ apply simp_all
+ done
+ moreover have "search_check (Execve p f fds # enrich_proc s p p') (up, rp, tp) f"
+ using p1 p2 p2' vd cf2sf f_in f_in' grant p3 f_in a1
+ apply (rule_tac s = s in enrich_search_check)
+ apply (simp_all add:is_file_simps)
+ apply (rule allI, rule impI, erule_tac x = fa in allE, simp)
+ apply (drule_tac ff = fa in cf2sfile_other')
+ by (auto simp:a2 curf_pre)
+ ultimately show ?thesis
+ using p1' p2' p3
+ apply (simp split:option.splits)
+ using grant p1 p2
+ apply simp
+ done
+ qed
+ ultimately show ?thesis using a1
+ by (erule_tac valid.intros(2), auto)
+ qed
+ qed
+ moreover have "\<And>tp fds. \<lbrakk>valid (Clone tp p fds # s); p' \<noteq> p; p' \<notin> all_procs s\<rbrakk> \<Longrightarrow>
+ valid (Clone tp p' (fds \<inter> proc_file_fds s tp) # Clone tp p fds # s)"
+ apply (frule vt_grant_os, frule vt_grant, drule not_all_procs_prop3)
+ apply (rule valid.intros(2))
+ apply (simp_all split:option.splits add:sectxt_of_obj_simps)
+ apply (auto simp add:proc_file_fds_def)[1]
+ apply (auto simp:inherit_fds_check_def sectxt_of_obj_simps sectxts_of_fds_def inherit_fds_check_ctxt_def)
+ done
+ moreover have "\<And>f flags fd opt. \<lbrakk>valid (Open p f flags fd opt # enrich_proc s p p');
+ is_created_proc s p; valid (Open p f flags fd opt # s); p' \<notin> all_procs s\<rbrakk>
+ \<Longrightarrow> valid (Open p' f (remove_create_flag flags) fd None # Open p f flags fd opt # enrich_proc s p p')"
+ proof-
+ fix f flags fd opt
+ assume a1: "valid (Open p f flags fd opt # enrich_proc s p p')" and a2: "is_created_proc s p"
+ and a3: "valid (Open p f flags fd opt # s)" and a4: "p' \<notin> all_procs s"
+ have cp2sp: "\<forall> tp. tp \<in> current_procs s \<longrightarrow> cp2sproc (enrich_proc s p p') tp = cp2sproc s tp"
+ and cf2sf: "\<forall> tf. tf \<in> current_files s \<longrightarrow> cf2sfile (enrich_proc s p p') tf = cf2sfile s tf"
+ and cfd2sfd: "\<forall> tp tfd. tfd \<in> proc_file_fds s tp \<longrightarrow> cfd2sfd (enrich_proc s p p') tp tfd = cfd2sfd s tp tfd"
+ and ffd_remain: "\<forall>tp fd f. file_of_proc_fd s tp fd = Some f \<longrightarrow>
+ file_of_proc_fd (enrich_proc s p p') tp fd = Some f"
+ and dup_sp: "cp2sproc (enrich_proc s p p') p' = cp2sproc s p"
+ and dup_sfd: "\<forall> fd. fd \<in> proc_file_fds s p \<longrightarrow> cfd2sfd (enrich_proc s p p') p' fd = cfd2sfd s p fd"
+ using pre a2 by auto
+ from a4 a3 have a0: "p' \<noteq> p" by (auto dest!:vt_grant_os not_all_procs_prop3 split:option.splits)
+ have a5: "p' \<in> current_procs (enrich_proc s p p')"
+ using a2 a3 vd
+ apply (erule_tac enrich_proc_dup_in)
+ by (simp_all add:vd a4)
+ have a6: "is_file (Open p f flags fd opt # enrich_proc s p p') f"
+ using a1 a3
+ by (auto simp:is_file_open dest:vt_grant_os)
+ have a7: "fd \<notin> current_proc_fds (enrich_proc s p p') p'"
+ using a2 a4 vd
+ apply (simp add:enrich_proc_dup_ffds_eq_fds)
+ apply (rule notI)
+ apply (drule_tac p = p in file_fds_subset_pfds)
+ apply (drule set_mp, simp)
+ using a3
+ apply (drule_tac vt_grant_os)
+ apply (auto split:option.splits)
+ done
+ from a1 have a8: "valid (enrich_proc s p p')" by (erule_tac valid.cases, auto)
+ from a3 have grant: "grant s (Open p f flags fd opt)" and os: "os_grant s (Open p f flags fd opt)"
+ by (auto dest:vt_grant_os vt_grant)
+ show "valid (Open p' f (remove_create_flag flags) fd None # Open p f flags fd opt # enrich_proc s p p')"
+ proof (cases opt)
+ case None
+ have f_in: "is_file (enrich_proc s p p') f"
+ proof-
+ from pre a2
+ have a4: "\<forall> obj. alive s obj \<longrightarrow> alive (enrich_proc s p p') obj"
+ by (auto)
+ show ?thesis using a3 a4 None
+ apply (erule_tac x = "O_file f" in allE)
+ by (auto dest:vt_grant_os)
+ qed
+ from grant None obtain up rp tp uf rf tf
+ where p1: "sectxt_of_obj s (O_proc p) = Some (up, rp, tp)"
+ and p2: "sectxt_of_obj s (O_file f) = Some (uf, rf, tf)"
+ apply (simp split:option.splits)
+ by (case_tac a, case_tac aa, blast)
+ have p1': "sectxt_of_obj (Open p f flags fd opt # enrich_proc s p p') (O_proc p') = Some (up, rp, tp)"
+ using p1 dup_sp a1
+ apply (simp add:sectxt_of_obj_simps)
+ by (simp add:cp2sproc_def split:option.splits)
+ from os None have f_in': "is_file s f" by simp
+ from vd os None have "\<exists> sf. cf2sfile s f = Some sf"
+ by (auto dest!:is_file_in_current current_file_has_sfile)
+ hence p2': "sectxt_of_obj (Open p f flags fd opt # enrich_proc s p p') (O_file f) = Some (uf, rf, tf)"
+ using p2 cf2sf os a1 None f_in' vd f_in
+ apply (erule_tac x = f in allE)
+ apply (auto dest:is_file_in_current simp:cf2sfile_def sectxt_of_obj_simps split:option.splits)
+ apply (case_tac f, simp)
+ apply (drule_tac s = s in root_is_dir', simp add:vd, simp+)
+ done
+ have "search_check (Open p f flags fd opt # enrich_proc s p p') (up, rp, tp) f"
+ using p1 p2 p2' vd cf2sf f_in f_in' grant f_in a1 None
+ apply (rule_tac s = s in enrich_search_check)
+ apply (simp_all add:is_file_simps)
+ apply (rule allI, rule impI, erule_tac x = fa in allE, simp)
+ apply (simp add:cf2sfile_open_none)
+ done
+ thus ?thesis using a0 a5 a6 a7 None a1
+ apply (rule_tac valid.intros(2))
+ apply (simp_all add:a1)
+ apply (case_tac flags, simp add:is_creat_excl_flag_def)
+ using p1' p2'
+ apply simp
+ using grant p1 p2
+ apply (simp add:oflags_check_remove_create)
+ done
+ next
+ case (Some inum)
+ with os obtain pf where parent: "parent f = Some pf" by auto
+ with grant Some obtain pu rp pt pfu pfr pft where
+ p1: "sectxt_of_obj s (O_proc p) = Some (pu, rp, pt)"
+ and p2: "sectxt_of_obj s (O_dir pf) = Some (pfu, pfr, pft)"
+ apply (simp split:option.splits)
+ apply (case_tac a, case_tac aa, blast)
+ done
+ from p1 have p1': "sectxt_of_obj (enrich_proc s p p') (O_proc p) = Some (pu, rp, pt)"
+ using cp2sp os
+ apply (erule_tac x = p in allE)
+ apply (auto split:option.splits simp:cp2sproc_def)
+ done
+ from os parent Some
+ have pf_in: "is_dir s pf" by auto
+ hence "\<exists> sf. cf2sfile s pf = Some sf" using vd
+ by (auto dest!:is_dir_in_current current_file_has_sfile)
+ from a1 parent Some have pf_in': "is_dir (enrich_proc s p p') pf"
+ apply (frule_tac vt_grant_os)
+ by (clarsimp)
+ have p2': "sectxt_of_obj (enrich_proc s p p') (O_dir pf) = Some (pfu, pfr, pft)"
+ proof-
+ have "cf2sfile (enrich_proc s p p') pf = cf2sfile s pf"
+ using cf2sf pf_in
+ apply (drule_tac is_dir_in_current)
+ apply (erule_tac x = pf in allE)
+ by simp
+ with pf_in pf_in' p2 vd Some a8
+ show ?thesis
+ apply (frule_tac is_dir_not_file)
+ apply (frule_tac s = "enrich_proc s p p'" in is_dir_not_file)
+ apply (simp add:cf2sfile_def)
+ apply (case_tac pf, simp)
+ apply (simp add:sroot_def root_sec_remains)
+ by (auto split:option.splits dest!:current_has_sec' get_pfs_secs_prop' dest:parentf_is_dir_prop1)
+ qed
+ from p1 have dup: "sectxt_of_obj (Open p f flags fd (Some inum) # enrich_proc s p p') (O_proc p')
+ = Some (pu, rp, pt)"
+ using a1 Some
+ apply (simp add:sec_open)
+ using dup_sp
+ apply (auto split:option.splits if_splits simp:cp2sproc_def)
+ done
+ have nsf: "sectxt_of_obj (Open p f flags fd (Some inum) # enrich_proc s p p') (O_file f)
+ = Some (pu, R_object, type_transition pt pft C_file True)"
+ using a1 Some p1 p2 parent p2' p1'
+ by (simp add:sec_open)
+ have "search_check (Open p f flags fd (Some inum) # enrich_proc s p p') (pu, rp, pt) f"
+ proof-
+ have "search_check (Open p f flags fd (Some inum) # enrich_proc s p p') (pu, rp, pt) pf"
+ using grant Some parent p1 p2 vd a1 pf_in pf_in' p2'
+ apply simp
+ apply (rule_tac s = s in enrich_search_check')
+ apply (simp_all add:is_dir_simps sectxt_of_obj_simps)
+ apply (rule allI, rule impI)
+ apply (case_tac "fa = f")
+ using os Some
+ apply simp
+ apply (drule_tac f' = fa in cf2sfile_open)
+ apply (simp add:current_files_simps)
+ using curf_pre a2
+ apply simp
+ apply simp
+ using cf2sf
+ apply simp
+ done
+ moreover have "is_file (Open p f flags fd (Some inum) # enrich_proc s p p') f"
+ using a1 Some
+ by (simp add:is_file_open)
+ ultimately
+ show ?thesis
+ using parent a1 Some nsf
+ apply (erule_tac search_check_leveling_f)
+ apply (simp_all)
+ apply (simp add:search_check_file_def)
+ apply (simp add:permission_check.simps)
+ sorry
+ qed
+ thus ?thesis using a0 a5 a6 a7 a1 Some
+ apply (rule_tac valid.intros(2))
+ apply (simp add:a1)
+ apply simp
+ apply (case_tac flags, simp add:is_creat_excl_flag_def)
+ using grant p1 p2 parent dup nsf
+ apply (simp add:oflags_check_remove_create)
+ done
+ qed
+ qed
+ moreover have "\<And>fd. \<lbrakk>valid (CloseFd p fd # enrich_proc s p p'); is_created_proc s p;
+ valid (CloseFd p fd # s); p' \<notin> all_procs s; fd \<in> proc_file_fds s p\<rbrakk>
+ \<Longrightarrow> valid (CloseFd p' fd # CloseFd p fd # enrich_proc s p p')"
+ proof-
+ fix fd
+ assume a1: "valid (CloseFd p fd # enrich_proc s p p')" and a2: "is_created_proc s p"
+ and a3: "p' \<notin> all_procs s" and a4: "valid (CloseFd p fd # s)"
+ and a5: "fd \<in> proc_file_fds s p"
+ from a4 a3 have a0: "p' \<noteq> p" by (auto dest!:vt_grant_os not_all_procs_prop3)
+ have "p' \<in> current_procs (enrich_proc s p p')"
+ using a2 a3 vd
+ by (auto intro:enrich_proc_dup_in)
+ moreover have "fd \<in> current_proc_fds (enrich_proc s p p') p'"
+ using a5 a2 a3 vd pre'
+ apply (simp)
+ apply (drule_tac s = "enrich_proc s p p'" and p = p' in file_fds_subset_pfds)
+ apply (erule set_mp)
+ apply (simp add:enrich_proc_dup_ffds)
+ done
+ ultimately show "valid (CloseFd p' fd # CloseFd p fd # enrich_proc s p p')"
+ apply (rule_tac valid.intros(2))
+ apply (simp_all add:a1 a0 a2 pre')
+ done
+ qed
+ moreover have "\<And> fd. \<lbrakk>valid (ReadFile p fd # enrich_proc s p p');
+ is_created_proc s p; valid (ReadFile p fd # s); p' \<notin> all_procs s\<rbrakk>
+ \<Longrightarrow> valid (ReadFile p' fd # ReadFile p fd # enrich_proc s p p')"
+ proof-
+ fix fd
+ assume a1: "valid (ReadFile p fd # enrich_proc s p p')" and a2: "is_created_proc s p"
+ and a3: "valid (ReadFile p fd # s)" and a4: "p' \<notin> all_procs s"
+ from a3 have os: "os_grant s (ReadFile p fd)" and grant: "grant s (ReadFile p fd)"
+ by (auto dest:vt_grant_os vt_grant)
+ have cp2sp: "\<forall> tp. tp \<in> current_procs s \<longrightarrow> cp2sproc (enrich_proc s p p') tp = cp2sproc s tp"
+ and cf2sf: "\<forall> tf. tf \<in> current_files s \<longrightarrow> cf2sfile (enrich_proc s p p') tf = cf2sfile s tf"
+ and cfd2sfd: "\<forall> tp tfd. tfd \<in> proc_file_fds s tp \<longrightarrow> cfd2sfd (enrich_proc s p p') tp tfd = cfd2sfd s tp tfd"
+ and ffd_remain: "\<forall>tp fd f. file_of_proc_fd s tp fd = Some f \<longrightarrow>
+ file_of_proc_fd (enrich_proc s p p') tp fd = Some f"
+ and dup_sp: "cp2sproc (enrich_proc s p p') p' = cp2sproc s p"
+ and dup_sfd: "\<forall> fd. fd \<in> proc_file_fds s p \<longrightarrow> cfd2sfd (enrich_proc s p p') p' fd = cfd2sfd s p fd"
+ using pre a2 by auto
+ have vd_enrich: "valid (enrich_proc s p p')" using a1 by (auto dest:valid.cases)
+ show "valid (ReadFile p' fd # ReadFile p fd # enrich_proc s p p')"
+ proof-
+ have "os_grant (ReadFile p fd # enrich_proc s p p') (ReadFile p' fd)"
+ using a1 a2 a4 vd os
+ apply (clarsimp simp:current_files_simps enrich_proc_dup_in enrich_proc_dup_ffds_eq_fds)
+ apply (simp add:proc_file_fds_def)
+ apply (rule conjI)
+ apply (rule_tac x = f in exI, simp add:enrich_proc_dup_ffd)
+ using curf_pre
+ apply (simp)
+ apply (drule enrich_proc_dup_fflags)
+ apply simp_all
+ apply (erule disjE)
+ apply auto
+ apply (simp add:is_read_flag_def)
+ done
+ moreover have "grant (ReadFile p fd # enrich_proc s p p') (ReadFile p' fd)"
+ proof-
+ from grant obtain f sp sfd sf where p1: "file_of_proc_fd s p fd = Some f"
+ and p2: "sectxt_of_obj s (O_proc p) = Some sp"
+ and p3: "sectxt_of_obj s (O_fd p fd) = Some sfd"
+ and p4: "sectxt_of_obj s (O_file f) = Some sf"
+ by (auto split:option.splits)
+ from os obtain flag where p0: "flags_of_proc_fd s p fd = Some flag"
+ by auto
+ from os have f_in_s: "f \<in> current_files s" using p1 by simp
+ from p1 vd have isfile_s: "is_file s f" by (erule_tac file_of_pfd_is_file, simp)
+ with alive_pre a2 have isfile_s': "is_file (enrich_proc s p p') f"
+ apply simp
+ apply (erule_tac x = "O_file f" in allE, simp)
+ done
+ from p0 obtain flag' where p0': "flags_of_proc_fd (enrich_proc s p p') p' fd = Some flag'"
+ and p0'': "(flag' = flag) \<or> (flag' = remove_create_flag flag)"
+ using a2 a4 vd
+ apply (drule_tac enrich_proc_dup_fflags)
+ apply auto
+ apply (case_tac flag, auto)
+ apply (case_tac flag, auto)
+ done
+ from p1 have p1': "file_of_proc_fd (enrich_proc s p p') p' fd = Some f"
+ using a2 a4 vd
+ by (simp add:enrich_proc_dup_ffd)
+ from p2 have p2': "sectxt_of_obj (enrich_proc s p p') (O_proc p') = Some sp"
+ using dup_sp
+ by (auto simp:cp2sproc_def split:option.splits)
+ from p3 p1 p1' p0 p0' os have p3': "sectxt_of_obj (enrich_proc s p p') (O_fd p' fd) = Some sfd"
+ using dup_sfd
+ apply (erule_tac x = fd in allE)
+ apply (auto simp:proc_file_fds_def cfd2sfd_def split:option.splits)
+ apply (drule current_file_has_sfile')
+ apply (simp add:vd, simp)
+ apply (drule current_file_has_sfile')
+ apply (simp add:vd, simp)
+ done
+ from p4 have p4': "sectxt_of_obj (enrich_proc s p p') (O_file f) = Some sf"
+ using f_in_s cf2sf isfile_s isfile_s' a1 vd_enrich vd
+ apply (erule_tac x = f in allE)
+ apply (simp)
+ apply (auto simp:cf2sfile_def split:option.splits
+ dest!:current_has_sec' get_pfs_secs_prop' dest:parentf_is_dir is_file_in_current)
+ apply (case_tac f, simp, drule root_is_dir', simp, simp, simp)
+ done
+ show ?thesis using p1' p2' p3' p4' a1
+ apply (simp add:sectxt_of_obj_simps)
+ using grant p1 p2 p3 p4
+ apply simp
+ done
+ qed
+ ultimately show ?thesis
+ using a1
+ by (erule_tac valid.intros(2), simp+)
+ qed
+ qed
+ ultimately show ?thesis
+ using created_cons vd_cons all_procs_cons
+ apply (case_tac e)
+ apply (auto simp:is_created_proc_simps split:if_splits)
+ done
+ qed
+ moreover have "\<forall>obj. alive (e # s) obj \<longrightarrow> alive (enrich_proc (e # s) p p') obj"
+ sorry
+ moreover have "\<forall>obj. enrich_not_alive (e # s) obj \<longrightarrow> enrich_not_alive (enrich_proc (e # s) p p') obj"
+ sorry
+ moreover have "files_hung_by_del (enrich_proc (e # s) p p') = files_hung_by_del (e # s)"
+ sorry
+ moreover have "\<forall>tp. tp \<in> current_procs (e # s) \<longrightarrow> cp2sproc (enrich_proc (e # s) p p') tp = cp2sproc (e # s) tp"
+ sorry
+ moreover have "\<forall>f. f \<in> current_files (e # s) \<longrightarrow> cf2sfile (enrich_proc (e # s) p p') f = cf2sfile (e # s) f"
+ sorry
+ moreover have "\<forall>q. q \<in> current_msgqs (e # s) \<longrightarrow> cq2smsgq (enrich_proc (e # s) p p') q = cq2smsgq (e # s) q"
+ sorry
+ moreover have "\<forall>tp fd f. file_of_proc_fd (e # s) tp fd = Some f \<longrightarrow>
+ file_of_proc_fd (enrich_proc (e # s) p p') tp fd = Some f"
+ sorry
+ moreover have "\<forall>tp fd flags. flags_of_proc_fd (e # s) tp fd = Some flags \<longrightarrow>
+ flags_of_proc_fd (enrich_proc (e # s) p p') tp fd = Some flags"
+ sorry
+ moreover have "\<forall>q. msgs_of_queue (enrich_proc (e # s) p p') q = msgs_of_queue (e # s) q"
+ sorry
+ moreover have "\<forall>tp fd. fd \<in> proc_file_fds (e # s) tp \<longrightarrow>
+ cfd2sfd (enrich_proc (e # s) p p') tp fd = cfd2sfd (e # s) tp fd"
+ sorry
+ moreover have "cp2sproc (enrich_proc (e # s) p p') p' = cp2sproc (e # s) p"
+ proof-
+ from pre have b0: "is_created_proc s p \<Longrightarrow> cp2sproc (enrich_proc s p p') p' = cp2sproc s p" by simp
+ have b1: "\<And> tp f fds. \<lbrakk>valid (enrich_proc (Execve tp f fds # s) p p'); valid (Execve tp f fds # s);
+ is_created_proc (Execve tp f fds # s) p; p' \<notin> all_procs (Execve tp f fds # s)\<rbrakk>
+ \<Longrightarrow> cp2sproc (enrich_proc (Execve tp f fds # s) p p') p' = cp2sproc (Execve tp f fds # s) p"
+ proof-
+ fix tp f fds
+ assume a1: "valid (enrich_proc (Execve tp f fds # s) p p')"
+ and a2: "valid (Execve tp f fds # s)" and a3: "is_created_proc (Execve tp f fds # s) p"
+ and a4: "p' \<notin> all_procs (Execve tp f fds # s)"
+ show "cp2sproc (enrich_proc (Execve tp f fds # s) p p') p' = cp2sproc (Execve tp f fds # s) p"
+ proof (cases "tp = p")
+ case True
+ show ?thesis using True a1 a2 a3 a4
+ thm not_all_procs_prop3
+ apply (auto simp add:cp2sproc_execve is_created_proc_def split:option.splits dest!:current_has_sec'
+ dest:vt_grant_os not_all_procs_prop2 not_all_procs_prop3)
+
+ sorry
+ next
+ case False
+ show ?thesis sorry
+ qed
+ qed
+ have b2: "\<And> tp fd. cp2sproc (enrich_proc (ReadFile tp fd # s) p p') p' = cp2sproc (ReadFile tp fd # s) p"
+ sorry
+ have b3: "\<And> tp. cp2sproc (enrich_proc (Exit tp # s) p p') p' = cp2sproc (Exit tp # s) p"
+ sorry
+ have b4: "\<And> tp tp'. cp2sproc (enrich_proc (Kill tp tp' # s) p p') p' = cp2sproc (Kill tp tp' # s) p"
+ sorry
+ have b5: "\<And> tp tp' fds. cp2sproc (enrich_proc (Clone tp tp' fds # s) p p') p' =
+ cp2sproc (Clone tp tp' fds # s) p"
+ sorry
+ have b6: "\<And> tp f flags fd opt. cp2sproc (enrich_proc (Open tp f flags fd opt # s) p p') p' =
+ cp2sproc (Open tp f flags fd opt # s) p"
+ sorry
+ have b7: "\<And> tp fd. cp2sproc (enrich_proc (CloseFd tp fd # s) p p') p' = cp2sproc (CloseFd tp fd # s) p"
+ sorry
+ show ?thesis using vd_enrich_cons
+ apply (case_tac e)
+ apply (simp_all only:b1 b2 b3 b4 b5 b6 b7)
+ using created_cons vd_enrich_cons vd_cons b0
+ apply (auto simp:cp2sproc_other is_created_proc_def)
+ done
+ qed
+ moreover have "\<forall> fd. fd \<in> proc_file_fds (e # s) p \<longrightarrow>
+ cfd2sfd (enrich_proc (e # s) p p') p' fd = cfd2sfd (e # s) p fd"
+ sorry
+ ultimately show ?case
+ by simp
+qed
+
+
+lemma enrich_proc_valid:
+ "\<lbrakk>valid s; is_created_proc s p; p' \<notin> all_procs s\<rbrakk> \<Longrightarrow> valid (enrich_proc s p p')"
+by (auto dest:enrich_proc_prop)
+
+lemma enrich_proc_valid:
+ "\<lbrakk>valid s; is_created_proc s p; p' \<notin> all_procs s\<rbrakk> \<Longrightarrow> "
+
+
+
+lemma enrich_proc_tainted:
+ "\<lbrakk>is_created_proc s p; p' \<notin> all_procs s; valid s\<rbrakk>
+ \<Longrightarrow> tainted (enrich_proc s p p') = (if (O_proc p \<in> tainted s)
+ then tainted s \<union> {O_proc p'} else tainted s)"
+apply (induct s)
+apply (simp add:is_created_proc_def)
+apply (frule vt_grant_os, frule vd_cons, simp)
+apply (frule enrich_proc_dup_in, simp+)
+apply (frule not_all_procs_prop3)
+apply (case_tac a)
+prefer 3
+apply (simp split:if_splits)
+apply (rule impI|rule conjI)+
+apply (simp add:is_created_proc_def)
+apply (auto simp:is_created_proc_def split:if_splits dest:tainted_in_current)[1]
+apply (simp add:is_created_proc_def)
+
+prefer 4
+apply (simp split:if_splits)
+apply (rule impI|rule conjI)+
+apply (simp add:is_created_proc_def)
+apply (auto simp:is_created_proc_def split:if_splits dest:tainted_in_current)[1]
+apply (simp add:is_created_proc_def)
+
+prefer 4
+apply (auto simp:is_created_proc_def split:if_splits option.splits dest:tainted_in_current)[1]
+
+prefer 4
+apply (auto simp:is_created_proc_def split:if_splits option.splits dest:tainted_in_current enrich_proc_dup_ffd enrich_proc_dup_ffd')[1]
+
+
+
+lemma enrich_proc_dup_tainted:
+ "\<lbrakk>is_created_proc s p; p' \<notin> all_procs s; valid s\<rbrakk>
+ \<Longrightarrow> (O_proc p' \<in> tainted (enrich_proc s p p')) = (O_proc p \<in> tainted s)"
+apply (induct s)
+apply (simp add:is_created_proc_def)
+apply (frule vt_grant_os, frule vd_cons)
+apply (case_tac a)
+apply (auto simp:is_created_proc_def)[1]
+
+
+lemma enrich_proc_tainted:
+ ""
+
+
+end
+
+end
\ No newline at end of file